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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/unwind/sstas.ma".
16 include "basic_2/computation/cprs.ma".
18 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
20 definition dxprs: ∀h. sd h → lenv → relation term ≝ λh,g,L,T1,T2.
21 ∃∃T. ⦃h, L⦄ ⊢ T1 •*[g] T & L ⊢ T ➡* T2.
23 interpretation "decomposed extended parallel computation (term)"
24 'DecomposedXPRedStar h g L T1 T2 = (dxprs h g L T1 T2).
26 (* Basic properties *********************************************************)
28 lemma dxprs_refl: ∀h,g,L. reflexive … (dxprs h g L).
31 lemma sstas_dxprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
34 lemma cprs_dxprs: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
37 lemma dxprs_strap1: ∀h,g,L,T1,T,T2.
38 ⦃h, L⦄ ⊢ T1 •*➡*[g] T → L ⊢ T ➡ T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
39 #h #g #L #T1 #T #T2 * /3 width=5/
42 lemma dxprs_strap2: ∀h,g,L,T1,T,T2,l.
43 ⦃h, L⦄ ⊢ T1 •[g] ⦃l+1, T⦄ → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
44 #h #g #L #T1 #T #T2 #l #HT1 * /3 width=4/